Local pixel-based methods have powerful regularization capability [1]}, [2]}, [3]}. However, in many applications, their suitability is limited by the type of signal they can promote. For example, total variation (TV) can preserve strong edges but promotes piecewise-constant solutions, and is hence less effective for capturing textures and geometrical patterns. In particular, TV cannot satisfactorily capture repetitive nonlocal structures such as textures. It has been demonstrated that this problem can be addressed using nonlocal regularization [4]}, [5]}, [6]}, [7]}, [8]}, i.e., by using image patches for comparison and by exploiting long-range similarities. A major bottleneck in using nonlocal regularization for remote sensing applications such as pansharpening and hyperspectral fusion is that the inversion process derived from such models is computationally intensive. We address this problem in the present work.
